Reconstruction of vector field from spherical harmonic coefficients

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SUMMARY

The discussion centers on the reconstruction of the acceleration vector g(r, theta, phi) from the JGM3 model of Earth's gravity, which utilizes coefficients C and S in Legendre polynomials to express gravitational potential U. The formula for U is given as U = ∑∑ CV + SW. A request for the specific algorithm to derive the acceleration vector from these coefficients was made, with a reference provided to a relevant paper by Hans Peter Schaub for further reading.

PREREQUISITES
  • Understanding of spherical harmonics and their application in gravitational modeling
  • Familiarity with the JGM3 model of Earth's gravity
  • Knowledge of Legendre polynomials and their role in potential theory
  • Basic concepts of vector calculus and polar coordinates
NEXT STEPS
  • Study the algorithm for calculating gravitational acceleration from spherical harmonic coefficients
  • Review the paper by Hans Peter Schaub on magnetic field reconstruction for insights into similar methodologies
  • Explore advanced topics in gravitational potential theory and its applications
  • Learn about numerical methods for evaluating spherical harmonics in geophysical contexts
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Geophysicists, researchers in gravitational modeling, and anyone involved in the analysis of Earth's gravitational field using spherical harmonics.

ronslow
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The JGM3 model of Earth's gravity is expressed in the form of coefficients C and S to Legendre polynomials in r, theta and phi which give the gravitational potential

U = [tex]\sum[/tex][tex]\sum[/tex] CV + SW

Can anyone tell me the algorithm for calculating acceleration vector g(r, theta, phi) from the coefficients, i.e. [tex]\Delta[/tex].U expressed as a polar vector?

Thanks

Robert
 
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Answer here:
http://homepage.mac.com/hanspeterschaub/work/Papers/UnderGradStudents/MagneticField.pdf
 
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